Particle swarm-differential evolution algorithm with multiple random mutation

Abstract

Differential evolution (DE) algorithm has attracted considerable attention because of its effectiveness and simplicity. However, previous studies have validated that DE still suffers from some limitations such as premature convergence and slow convergence especially dealing with multimodal optimization problems. To address these concerning issues, we propose an innovative optimization method named particle swarm-differential evolution algorithm with multiple random mutation (MRPSODE) in this paper. The proposed MRPSODE algorithm is based on multiple random mutation framework cooperating with mean particle swarm mutation strategy, DE/current-to-rand/1 mutation strategy and disturbance strategy. Firstly, we incorporate the modified mean particle swarm mutation strategy into DE algorithm to improve the global convergence ability. Secondly, DE/current-to-rand/1 mutation strategy is adopted to increase the population diversity and produce perturbations to avoid the algorithm trapping into a local optimum. Thirdly, we propose a disturbance strategy to help the population escape from local optima, so as to enhance the exploration ability. Finally, to ensure that the proposed algorithm can get satisfactory solutions with a fast convergence speed, we design a multiple random mutation framework, in which these three mutation strategies can effectively play their advantages and make up for the shortcomings of others. To evaluate the performance of the proposed algorithm, three different experiments are constructed on twenty-nine classical benchmark functions. The simulation results demonstrate that, (1) MRPSODE significantly outperforms conventional PSO and DE algorithms, (2) MRPSODE can achieve better performance than nine well-known DE variants in terms of solution quality and robustness, (3) MRPSODE is superior to nine latest heuristic-based algorithms. Furthermore, MRPSODE is successfully applied to seven typical constrained optimization problems and performs better than almost all compared methods.